260 DOC.

21

THEORY OF RELATIVITY

[21]

II. The General

Theory

of

Relativity

The

special theory

of

relativity

is

based

on

the fundamental idea that certain

coordinate

systems (inertial systems)

are

equivalent

for the

formulation

of

physical

laws;

these

are

those coordinate

systems

with

respect

to

which the law of inertia and

the law of

constancy

of the

velocity

of

light

in

vacuum

claim

validity.

Are these

systems

indeed

privileged

in

nature,

or

does

this

privileged status stem

from

an

incomplete understanding

of the laws of nature? To be

sure,

according

to

Galileo's

law of

inertia,

the inertial

systems

seem

to

be

privileged

over

coordinate

systems

that

move

in

a

different

manner.

But

the law of

inertia has

a

serious

deficiency

that makes

the

cogency

of this

argument

appear

doubtful.

Let

us imagine a portion

of

space

that

is

entirely

force-free

in

the

sense

of

classical

mechanics, thus,

a

space

from which

gravitating

masses are

far removed.

Then,

according

to mechanics,

there exists

an

inertial

system

K,

with

respect

to

which

a mass

M that

is

left to itself

moves

rectilinearly

and

uniformly through

the

portion

of

space

under consideration. If

one now

introduces

a

coordinate

system

K'

that

is

uniformly

accelerated with

respect

to

K,

then the

mass

M,

which

is

left

to itself,

does

not

move

in

a straight

line with

respect

to

K'

but, rather,

along

a

parabola,

akin

to

the

way

in which

a mass near

the surface of the earth

moves,

relative

to

it,

under the

influence of

gravity.

Can

one

draw from this the conclusion that K'

is

(absolutely)

accelerated? This

conclusion would

not

be

justified.

One

can

just as

well

view K'

as

being

"at rest"

provided

that

one assumes

the

presence,

with

respect

to K',

of

a

uniform

gravitational

field,

which

is

seen as

the

reason

why

the bodies

move

in

an

accelerated fashion with

respect

to

K'.

To be

sure, it

could be

argued against

such

a

conception

that

one

cannot

indicate

the

masses

that

create

this

gravitational

field. But without

violating

the fundamental

principles

of Newtonian

mechanics,

one can imagine

that these

masses are

practically

infinitely

distant.

Besides,

we

do

not

know

to

what

degree

of

exactness

the

Newtonian

law of

gravitation corresponds

to

the

truth.

There

is

one

circumstance that

speaks forcefully

for

our

conception.

All

masses

fall with the

same

acceleration with

respect

to K'

independently

of their

particular

physical

and chemical

nature.

Experience

shows that the

same

holds

true, indeed,

with

extraordinary accuracy,

with

respect

to

the

gravitational

field.

In

light

of

the

remarkable fact that

we

recognize

in

the

gravitational

field

a physical

state

of

space

that

brings

about the

same

behavior of bodies

as

that which obtains with

respect

to

K',

the

hypothesis seems

completely

natural

that,

with

respect

to

K',

there exists

a

gravitational

field that

is

essentially

identical

to

the

gravitational

fields

generated by

masses

according

to

Newton's

law.